The oblique azimuthal projection of geodesic type for the biaxial ellipsoid: Riemann polar and normal coordinates     

E. W. Grafarend  R. Syffus 《Journal of Geodesy》1995,70(1-2):13-37

Summary Riemann polar/normal coordinates are the constituents to generate the oblique azimuthal projection of geodesic type, here applied to the reference ellipsoid of revolution (biaxial ellipsoid).Firstly we constitute a minimal atlas of the biaxial ellipsoid built on {ellipsoidal longitude, ellipsoidal latitude} and {metalongitude, metalatitude}. TheDarboux equations of a 1-dimensional submanifold (curve) in a 2-dimensional manifold (biaxial ellipsoid) are reviewed, in particular to represent geodetic curvature, geodetic torsion and normal curvature in terms of elements of the first and second fundamental form as well as theChristoffel symbols. The notion of ageodesic anda geodesic circle is given and illustrated by two examples. The system of twosecond order ordinary differential equations of ageodesic (Lagrange portrait) is presented in contrast to the system of twothird order ordinary differential equations of ageodesic circle (Proofs are collected inAppendix A andB). A precise definition of theRiemann mapping/mapping of geodesics into the local tangent space/tangent plane has been found.Secondly we computeRiemann polar/normal coordinates for the biaxial ellipsoid, both in theLagrange portrait (Legendre series) and in theHamilton portrait (Lie series).Thirdly we have succeeded in a detailed deformation analysis/Tissot distortion analysis of theRiemann mapping. The eigenvalues — the eigenvectors of the Cauchy-Green deformation tensor by means of ageneral eigenvalue-eigenvector problem have been computed inTable 3.1 andTable 3.2 (₁, ₂ = 1) illustrated inFigures 3.1, 3.2 and3.3. Table 3.3 contains the representation ofmaximum angular distortion of theRiemann mapping. Fourthly an elaborate global distortion analysis with respect toconformal Gau-Krüger, parallel Soldner andgeodesic Riemann coordinates based upon theAiry total deformation (energy) measure is presented in a corollary and numerically tested inTable 4.1. In a local strip [-l _E,l _E] = [-2°, +2°], [b _S,b _N] = [-2°, +2°]Riemann normal coordinates generate the smallest distortion, next are theparallel Soldner coordinates; the largest distortion by far is met by theconformal Gau-Krüger coordinates. Thus it can be concluded that for mapping of local areas of the biaxial ellipsoid surface the oblique azimuthal projection of geodesic type/Riemann polar/normal coordinates has to be favored with respect to others.  相似文献   

Physical conditions in eruptive prominences at several solar radii     

Rainer M. E. Illing  R. Grant Athay 《Solar physics》1986,105(1):173-190

SMM data from the Corograph/Polarimeter experiment giving intensities of H and continuum emission in eight erupting prominences are analyzed to obtain the physical conditions in the regions of H emission. Since the H intensity depends upon three unknowns whereas only two independent observations are available, it is necessary to assume one additional condition in order to obtain unique solutions. Solutions are chosen that give the maximum expansion of the prominence volume as reflected by minimum values of the electron density. These solutions correspond closely with those giving the best agreement between the gas pressure in the prominence and the ambient coronal pressure. Electron densities are found to be of the order of 10⁸ cm^-3 at temperatures near 2 × 10⁴ K.The National Center for Atmospheric Research is operated by the University Corporation for Atmospheric Research under sponsorship of the National Science Foundation.  相似文献   

Clay mineral distribution in surface sediments of the South Atlantic: sources, transport, and relation to oceanography   总被引：2，自引：0，他引：2  

Rainer Petschick  Gerhard Kuhn  Franz Gingele 《Marine Geology》1996,130(3-4):203-229

Surface samples, mostly from abyssal sediments of the South Atlantic, from parts of the equatorial Atlantic, and of the Antarctic Ocean, were investigated for clay content and clay mineral composition. Maps of relative clay mineral content were compiled, which improve previous maps by showing more details, especially at high latitudes. Large-scale relations regarding the origin and transport paths of detrital clay are revealed. High smectite concentrations are observed in abyssal regions, primarily derived from southernmost South America and from minor sources in Southwest Africa. Near submarine volcanoes of the Antarctic Ocean (South Sandwich, Bouvet Island) smectite contents exhibit distinct maxima, which is ascribed to the weathering of altered basalts and volcanic glasses. The illite distribution can be subdivided into five major zones including two maxima revealing both South African and Antarctic sources. A particularly high amount of Mg- and Fe-rich illites are observed close to East Antarctica. They are derived from biotite-bearing crystalline rocks and transported to the west by the East Antarctic Coastal Current. Chiorite and well-crystallized dioctaedral illite are typical minerals enriched within the Subantarctic and Polarfrontal-Zone but of minor importance off East Antarctica. Kaolinite dominates the clay mineral assemblage at low latitudes, where the continental source rocks (West Africa, Brazil) are mainly affected by intensive chemical weathering. Surprisingly, a slight increase of kaolinite is observed in the Enderby Basin and near the Filchner-Ronne Ice shelf.

The investigated area can be subdivided into ten, large-scale clay facies zones with characteristic possible source regions and transport paths. Clay mineral assemblages of the largest part of the South Atlantic, especially of the western basins are dominated by chlorite and illite derived from the Antarctic Peninsula and southernmost South America and supported by advection within the Circumantarctic Deep Water flow. In contrast, the East Antarctic provinces are relatively small. Assemblages of the eastern basins north of 30°S are strongly influenced by African sources, controlled by weathering regimes on land and by a complex interaction of wind, river and deep ocean transport. The strong gradient in clay mineral composition at the Brazilian slope indicate a relatively low contribution of tropically derived assemblages to the western basins.  相似文献   

Biosiliceous particle flux in the Southern Ocean     

Andrea Abelmann  Rainer Gersonde 《Marine Chemistry》1991,35(1-4)

The flux of diatom valves and radiolarian shells obtained during short-term and annual sediment trap experiments at seven localities in the Atlantic sector of the Antarctic Ocean (in the Drake Passage, Bransfield Strait, Powell Basin, NW and SE Weddell Sea and the Polar Front north of Bouvet Island) is summarized and discussed. The deployment of time-series sediment traps provided annual flux records between 1983 and 1990. The biosiliceous particle flux is characterized by significant seasonal and interannual variations. Flux pulses, accounting for 70–95% of the total annual flux, occur during austral summer, with a duration ranging between about 2 and 9 weeks. The annual values of vertical diatom and radiolarian flux range between 0.26 × 10⁹ and more than 26 × 10⁹ valves m⁻² and between 0.21 × 10⁴ and 70 × 10⁴ shells m⁻², respectively. Interannual differences in the particle flux range over a factor of 10. Grazers play an important role in controlling the quantity, timing and pattern of the vertical biosiliceous particle flux.The flux pattern of diatoms and radiolarians is similar at most of the sites investigated and shows a close relationship between the production of siliceous phytoplankton and proto-zooplankton. At some sites, however, the radiolarian flux pattern indicates probably phytoplankton production which is not documented by direct signals in the trap record.During their transfer through the water column to the ocean floor, the composition of the biosiliceous particles is altered mechanically (breakdown by grazing Zooplankton) and by dissolution, which significantly affects especially diatoms and phaeodarians in the upper portion of the water column and at the sediment-water interface.Significant lateral transport of suspended biosiliceous particles was observed in the bottom water layer in regions adjacent to shelf areas (Bransfield Strait), and in the vicinity of topographic elevations (Maud Rise), indicating considerable redistribution of biogenic silica in these regions.  相似文献   

Book Review of Advances in Nonlinear Dynamos,by Antonio Ferriz-Mas and Manuel Núñez,The Fluid Mechanics of Astrophysics and Geophysics,Vol. 9, Series Editors A.M. Soward and M. Ghil,Taylor and Francis,London, New York, 2003, IX + 384 pp., £80.00, hardback (ISBN 0-415-28788-X)     

Rainer Hollerbach 《地球物理与天体物理流体动力学》2013,107(5):419-420

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On the energetics of magnetic instabilities     

Rainer Hollerbach 《地球物理与天体物理流体动力学》2013,107(3-4):211-213

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Rainfall interception in a lower montane forest in Ecuador: effects of canopy properties     

Katrin Fleischbein  Wolfgang Wilcke  Rainer Goller  Jens Boy  Carlos Valarezo  Wolfgang Zech  Klaus Knoblich 《水文研究》2005,19(7):1355-1371

Rainfall interception in forests is influenced by properties of the canopy that tend to vary over small distances. Our objectives were: (i) to determine the variables needed to model the interception loss of the canopy of a lower montane forest in south Ecuador, i.e. the storage capacity of the leaves S and of the trunks and branches S_t, and the fractions of direct throughfall p and stemflow p_t; (ii) to assess the influence of canopy density and epiphyte coverage of trees on the interception of rainfall and subsequent evaporation losses. The study site was located on the eastern slope of the eastern cordillera in the south Ecuadorian Andes at 1900–2000 m above sea level. We monitored incident rainfall, throughfall, and stemflow between April 1998 and April 2001. In 2001, the leaf area index (LAI), inferred from light transmission, and epiphyte coverage was determined. The mean annual incident rainfall at three gauging stations ranged between 2319 and 2561 mm. The mean annual interception loss at five study transects in the forest varied between 591 and 1321 mm, i.e. between 25 and 52% of the incident rainfall. Mean S was estimated at 1·91 mm for relatively dry weeks with a regression model and at 2·46 mm for all weeks with the analytical Gash model; the respective estimates of mean S_t were 0·04 mm and 0·09 mm, of mean p were 0·42 and 0·63, and of mean p_t were 0·003 and 0·012. The LAI ranged from 5·19 to 9·32. Epiphytes, mostly bryophytes, covered up to 80% of the trunk and branch surfaces. The fraction of direct throughfall p and the LAI correlated significantly with interception loss (Pearson's correlation coefficient r = −0·77 and 0·35 respectively, n = 40). Bryophyte and lichen coverage tended to decrease S_t and vascular epiphytes tended to increase it, although there was no significant correlation between epiphyte coverage and interception loss. Our results demonstrate that canopy density influences interception loss but only explains part of the total variation in interception loss. Copyright © 2004 John Wiley & Sons, Ltd.  相似文献   

    

Rainer Sauerborn 《Global Change & Human Health》2001,2(2):119

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Moon and Earth : compositional differences inferred from siderophiles,volatiles, and alkalis in basalts     

Rainer Wolf  Edward Anders 《Geochimica et cosmochimica acta》1980,44(12):2111-2124

We have compared RNAA analyses of 18 trace elements in 25 low-Ti lunar and 10 terrestrial oceanic basalts. According to Ringwood and Kesson, the abundance ratio in basalts for most of these elements approximates the ratio in the two planets.Volatiles (Ag, Bi, Br, Cd, In, Sb, Sn, Tl, Zn) are depleted in lunar basalts by a nearly constant factor of 0.026 ± 0.013, relative to terrestrial basalts. Given the differences in volatility among these elements, this constancy is not consistent with models that derive the Moon's volatiles from partial recondensation of the Earth's mantle or from partial degassing of a captured body. It is consistent with models that derive planetary volatiles from a thin veneer (or a residuum) of C-chondrite material; apparently the Moon received only 2.6% of the Earth's endowment of such material per unit mass.Chalcogens (Se and Te) have virtually constant and identical abundances in lunar and terrestrial basalts, probably reflecting saturation with Fe(S, Se, Te) in the source regions.Siderophiles show diverse trends. Ni is relatively abundant in lunar basalts (4 × 10^?3 × Cl-chondrites), whereas Ir, Re, Ge, Au are depleted to 10^?4?10^?5× Cl. Except for Ir, these elements are consistently enriched in terrestrial basalts: Ni 3 × , Re 370 ×, Ge 330 × , Au 9 × . This difference apparently reflects the presence of nickel-iron phase in the lunar mantle, which sequesters these metals. On Earth, where such metal is absent, these elements partition into the crust to a greater degree. Though no lunar mantle rock is known, an analogue is provided by the siderophile-rich dunite 72417 (~0.1% metal) and the complementary, siderophile-poor troctolite 76535. The implied metal-siderophile distribution coefficients range from 10⁴ to 10⁶, and are consistent with available laboratory data.The evidence does not support the alternative explanation advanced by Ringwood—that Re was volatilized during the Moon's formation, and is an incompatible element (like La or W⁴⁺) in igneous processes. Re is much more depleted than elements of far greater volatility: (Re/U)_Cl～- 4 × 10^?6 vs (T1/U)_Cl = 1.3 × 10^?4, and Re does not correlate with La or other incompatibles.Heavy alkalis (K, Rb, Cs) show increasing depletion with atomic number. Cs/Rb ratios in lunar basalts, eucrites, and shergottites are 0.44, 0.36, and 0.65 × Cl, whereas the value for the bulk Earth is 0.15–0.26. These ratios fall within the range observed in LL and E6 chondrites. supporting the suggestion that the alkali depletion in planets, as in chondrites, was caused by localized remelting of nebular dust (= chondrule formation). Indeed, the small fractionation of K, Rb and Cs, despite their great differences in volatility, suggests that the planets, like the chondrites, formed from a mixture of depleted and undepleted material, not from a single, partially devolatilized material.  相似文献   

Characterization of sediments in an abandoned mining area; a case study of Mansfeld region,Germany   总被引：1，自引：0，他引：1  

Rainer?WennrichEmail author  Jürgen?Mattusch  Peter?Morgenstern  Klaus?Freyer  Hanns-Christian?Treutler  Hans-Joachim?St?rk  Lutz?Brüggemann  Albrecht?Paschke  Birgit?Daus  Holger?Weiss 《Environmental Geology》2004,45(6):818-833

The distribution of selected heavy metals, including some radionuclides, metalloids and non-metals was determined in stream sediments in a region influenced by abandoned copper mining and ore processing activities. A considerable amount of the ore processing waste with a very complex composition and highly elevated concentrations of zinc, sulfur, lead, copper, arsenic, and a lot of other elements in the range between 100 and 1,000 mg/kg (Sb, Mn, Ni, Cr, Cd, Hg, and Ag) was piled up on mine dumps. The dispersion of the pollutants originating from this source and their environmental impact were investigated. Both, sediments and original waste material were studied to indicate the pathways and the mobilization behavior of different pollutants. For this purpose, the process of the elution of pollutants by application of different fractionation schemes was studied. The capabilities of different analytical techniques are shown for the analysis of solid samples (X-ray fluorescence spectrometry, Gamma-spectrometry) and liquid ones (ICP-atomic emission spectrometry, ICP-mass spectrometry and different techniques of atomic absorption). Additionally, the coupling of ion chromatography and ICP-MS detection was used to study the distribution of arsenic species in the sediment cores of a lake which acts as a natural sink for the region.  相似文献